<p>In the diagram, the smaller circle has centre \(O\) and intersects the larger circle at \(B\) and \(C\). The point \(O\) also lies on the larger circle. \(ABD\) and \(ACE\) are straight lines, where&nbsp;\(A\) is on the smaller circle and \(D, E\) are on the larger circle. \(F\) is the point of intersection of \(BE\) and \(CD\). Prove that</p>
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<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">angle \(AEB = 180^\circ - 2 \times\) angle \(BAC\) ,</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">triangle \(ABE\) is an isosceles triangle, and</div></li><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph">angle \(DFE = 360^\circ - 3 \times\) angle \(BAC\) .</div></li></ol>

In the diagram, the smaller circle has centre \(O\) and intersects the larger circle at \(B\) and \(C\). The point \(O\) also lies on the larger circle. \(ABD\) and \(ACE\) are straight lines, where \(A\) is on the smaller circle and \(D, E\) are on the larger circle. \(F\) is the point of intersection of \(BE\) and \(CD\). Prove that

angle \(AEB = 180^\circ - 2 \times\) angle \(BAC\) ,

triangle \(ABE\) is an isosceles triangle, and

angle \(DFE = 360^\circ - 3 \times\) angle \(BAC\) .

Polygons - Properties of Special Triangles

Polygons - Properties of Special Triangles

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